After starting from the third spot following Lewis Hamilton's three-place grid drop for a yellow flag infringement, Norris had a disappointing race start as he dropped fifth in few laps.
During the closing part of the race, Norris had the opportunity to fight for the podium, since Hamilton and Perez got five seconds penalties for contact with Alexander Albon and pitlane speeding, respectively.
Norris passed the Racing Point at turn 3 to get some fresh air and post the fastest lap, maintaining a 4.8s distance from Hamilton and ending up third.
Interviewed after the race, Norris remarked that he thought that he could lose his chance to score hao first podium.
"I dropped to fifth with a few laps to go, Carlos [Sainz] was almost going to get past me.
"But I didn't give up and I managed to get past Perez and ended up on the podium.
"I mean it's a long race, but I kept going and kept giving my all, [I had] a pretty cool last few laps trying to push as much as I can. I am a bit out of breath, but I am so happy and proud of the team.
"Considering where we were a few years ago to now, I think it's a pretty good achievement, so I'm proud to be part of it."
Norris concluded, pointing out that he needed to overtake Perez to avoid attacks from behind as he was struggling behind the racing point. Norris remarked that he did not know about Hamilton's penalty at that moment.
"The last few laps, when I had to get past Checo, I knew he had a five-second penalty but nothing more than that," he added.
"I always seemed to struggle when I was close to the cars ahead and more vulnerable to the guys behind.
"So I knew - not just because of Lewis because I didn't know at the time [he had a penalty], I knew I had to try to get past him.
"And then when the Lewis penalty came, I knew I had to turn it up a little bit."